A factor of a number will divide that number exactly, without any remainder.
Example : 2 is a factor of 16 because 2 goes into 16 exactly 8 times, with no remainder.
But note that 16 also has other factors apart from 2. These other factors are
- 4 : which goes into 16 exactly 4 times
- 8 : which goes into 16 exactly 2 times
- as well as 16 itself : 16 divided by 16 equals 1
- and also 1 : 16 divided by 1 equals 16
So the number 16 has a total of 5 factors.
Example : 24 has the following factors
Example : 3 is a factor of 9 because 3 divides into 9 exactly, without any remainder.
Example : 3 is also a factor of
27, 18, 30, 15,....and many more
Which of the following are factors of 72 ?
4 is a factor of which of these numbers ?
Highest Common Factor
The Highest Common Factor (HCF) of two numbers is the highest number that is a factor of both numbers
Example : The numbers 36 and 24 have a common factor of 4. But this not the Highest Common Factor, because 6 is also a common factor. The number 6 itself is still not the required HCF - the HCF is actually 12.
Finding Factors of Large Numbers
First the easier ones
- 2 is a factor of all even numbers
- 10 is a factor of all numbers ending in 0
- 5 is a factor of all numbers ending in a 0 or 5
- 3 is a factor
of a number if it is also a factor of the sum of the individual digits in the number, e.g
- 65421 (digits add up to 18)
- 24 (digits add up to 6)
- 321 (digits add up to 6)
- 9 is a factor of a number if it is also a factor of the sum of the individual
digits in the number, e.g.
- 76437 (digits add up to 27)
- 27 (digits add up to 9)
- 981 (digits add up to 18)
- 11 is a factor of a three figure number if the middle digit is the sum of the two outside digits, e.g. 792
Multiples of a number are obtained just by multiplying that number by a whole number.
Example The multiples of 6 are
6, 12 , 18, 24, 30, etc
Note that 6 is a multiple of 6 because it is equal to 6 multiplied by one.
Which of the following are multiples of 7 ?
Lowest Common Multiple
The Lowest Common Multiple (LCM) of two numbers is a multiple of both numbers and lower than all other numbers that are also multiples of both the numbers.
Example The Lowest Common Multiple of 6 and 4 is 12.
12 is lower than other common multiples like 24, 36, 48, and there is no common multiple of 6 and 4 which is lower than 12.